KD-Tree

Author: Dev-XYS

K-Dimensional-Tree.cpp

@@ -0,0 +1,164 @@
+// Problem Name: SJY摆棋子
+// Algorithm: KD-Tree
+
+#include <cstdio>
+#include <algorithm>
+
+#define NIL 0
+#define INF 1000000000
+
+using namespace std;
+
+struct point
+{
+	int co[2];
+	point(int x = 0, int y = 0) { co[0] = x, co[1] = y; }
+	int& operator [] (int x) { return co[x]; }
+	const int& operator [] (int x) const { return co[x]; }
+}d[500010];
+
+struct node
+{
+	node *lch, *rch;
+	point p;
+	int min[2], max[2];
+	node(point _p = point()) : lch(NIL), rch(NIL), p(_p) { /*min[0] = min[1] = INF, max[0] = max[1] = -INF;*/ }
+}*root;
+
+inline int abs(int x)
+{
+	return x < 0 ? -x : x;
+}
+
+inline int dist(point &x, point &y)
+{
+	return abs(x.co[0] - y.co[0]) + abs(x.co[1] - y.co[1]);
+}
+
+int _d_;
+inline bool _point_cmp_(const point &x, const point &y)
+{
+	if (x[_d_] == y[_d_]) return x[_d_ ^ 1] < y[_d_ ^ 1];
+	return x[_d_] < y[_d_];
+}
+
+inline void update(node *u)
+{
+	if (u->lch != NIL)
+	{
+		u->min[0] = min(u->min[0], u->lch->min[0]);
+		u->min[1] = min(u->min[1], u->lch->min[1]);
+		u->max[0] = max(u->max[0], u->lch->max[0]);
+		u->max[1] = max(u->max[1], u->lch->max[1]);
+	}
+	if (u->rch != NIL)
+	{
+		u->min[0] = min(u->min[0], u->rch->min[0]);
+		u->min[1] = min(u->min[1], u->rch->min[1]);
+		u->max[0] = max(u->max[0], u->rch->max[0]);
+		u->max[1] = max(u->max[1], u->rch->max[1]);
+	}
+}
+
+void build(node *&u, int l, int r, int dim)
+{
+	if (l == r)
+	{
+		u = new node(d[l]);
+		u->min[0] = u->max[0] = d[l][0];
+		u->min[1] = u->max[1] = d[l][1];
+	}
+	else if (l < r)
+	{
+		int mid = (l + r) >> 1;
+		_d_ = dim;
+		nth_element(d + l, d + mid, d + r + 1, _point_cmp_);
+		u = new node(d[mid]);
+		u->min[0] = u->max[0] = d[mid][0];
+		u->min[1] = u->max[1] = d[mid][1];
+		build(u->lch, l, mid - 1, dim ^ 1);
+		build(u->rch, mid + 1, r, dim ^ 1);
+		update(u);
+	}
+}
+
+void insert(node *&u, point p, int dim)
+{
+	if (u == NIL)
+	{
+		u = new node(p);
+		u->min[0] = u->max[0] = p[0];
+		u->min[1] = u->max[1] = p[1];
+		return;
+	}
+	if (p[dim] <= u->p[dim]) insert(u->lch, p, dim ^ 1);
+	else insert(u->rch, p, dim ^ 1);
+	update(u);
+}
+
+int get_dis(point p, node *u)
+{
+	int res = 0;
+	if (p[0] < u->min[0]) res += u->min[0] - p[0];
+	if (p[0] > u->max[0]) res += p[0] - u->max[0];
+	if (p[1] < u->min[1]) res += u->min[1] - p[1];
+	if (p[1] > u->max[1]) res += p[1] - u->max[1];
+	return res;
+}
+
+int mindis;
+void find(node *u, point p, int dim)
+{
+	if (u == NIL) return;
+	int dis = dist(p, u->p);
+	if (dis < mindis) mindis = dis;
+	int dl = INF, dr = INF;
+	if (u->lch != NIL) dl = get_dis(p, u->lch);
+	if (u->rch != NIL) dr = get_dis(p, u->rch);
+	if (dl < dr)
+	{
+		if (dl < mindis) find(u->lch, p, dim ^ 1);
+		if (dr < mindis) find(u->rch, p, dim ^ 1);
+	}
+	else
+	{
+		if (dr < mindis) find(u->rch, p, dim ^ 1);
+		if (dl < mindis) find(u->lch, p, dim ^ 1);
+	}
+}
+
+void dfs(node *u)
+{
+	if (u == NIL) return;
+	printf("dfs : (%d, %d)\n", u->p[0], u->p[1]);
+	dfs(u->lch);
+	dfs(u->rch);
+}
+
+int main()
+{
+	int n, m;
+	scanf("%d%d", &n, &m);
+	for (int i = 0; i < n; i++)
+	{
+		scanf("%d%d", &d[i][0], &d[i][1]);
+	}
+	build(root, 0, n - 1, 0);
+	int op, x, y;
+	while (m--)
+	{
+		scanf("%d%d%d", &op, &x, &y);
+		if (op == 1)
+		{
+			insert(root, point(x, y), 0);
+		}
+		else
+		{
+			mindis = INF;
+			find(root, point(x, y), 0);
+			if (mindis < INF) printf("%d\n", mindis);
+			else printf("INF\n");
+		}
+	}
+	return 0;
+}